Time series distance metric

Question

In order to clusterize a set of time series I'm looking for a smart distance metric. I've tried some well known metric but no one fits to my case.

ex: Let's assume that my cluster algorithm extracts this three centroids [s1, s2, s3]:

I want to put this new example [sx] in the most similar cluster:

The most similar centroids is the second one, so I need to find a distance function d that gives me d(sx, s2) < d(sx, s1) and d(sx, s2) < d(sx, s3)

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Here the results with metrics [cosine, euclidean, minkowski, dynamic type warping] ]3

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User Pietro P suggested to apply the distances on the cumulated version of the time series The solution works, here the plots and the metrics:

Answer 1

nice question! using any standard distance of R^n (euclidean, manhattan or generically minkowski) over those time series cannot achieve the result you want, since those metrics are independent of the permutations of the coordinate of R^n (while time is strictly ordered and it is the phenomenon you want to capture).

A simple trick, that can do what you ask is using the cumulated version of the time series (sum values over time as time increases) and then apply a standard metric. Using the Manhattan metric, you would get as a distance between two time series the area between their cumulated versions.

Answer 2

Another approach would be by utilizing DTW which is an algorithm to compute the similarity between two temporal sequences. Full disclosure; I coded a Python package for this purpose called trendypy, you can download via pip (pip install trendypy). Here is a demo on how to utilize the package. You're just just basically computing the total min distance for different combinations to set the cluster centers.